IB Math Methods Syllabus

For Examinations beginning in May 2000

All topics in the core are compulsory. Candidates are required to study all the sub-topics in each of the six topics in this part of the syllabus.

1. Number and Algebra (10 hours)
   • Number Sets
   • Arithmetic and Geometric Sequences and Series
   • Exponents and Logarithms
   • BInomial Theorem
2. Functions and Equations (25 hours)
   • Domain, Range, Function Notation, Inverse Functions
   • Graphing and Use of Graphic Calculators to Estimate Solutions
   • Transformations of Graphs - Reflections, Stretches and Translations
   • Treatment of Following Functions
     • Linear
     • Quadratic in Standard Form
     • Reciprocal
     • Exponential including base e
     • Logarithmic including natural log
3. Circular Functions and Trigonometry (15 hours)
   • Radian Measure, Arc Length and Sector Area
   • Unit Circle Definition of Sine, Cosine and Tangent, Double Angle Formula
   • Circular Functions of Sine, Cosine and Tangent and the Inverses including Changes in Amplitude, Period and Phase Shifts
   • Sine and Cosine Rule and Area of a Triangle for Non-Right Triangles
4. Vector Geometry (15 hours)
   • Column Representation of a Vector, Sums, Scalar Multiplication, Magnitutde and Position Vectors
   • Dot (Scalar) Product - Properties and Relation to Slopes and Angles
   • Vector Representation of a Line
5. Statistics and Probability (20 hours)
   • Treatment of Discrete, Continuous, Grouped and Simple Data
   • Methods of Display
     • Frequency Tables and Histograms
     • Cumulative Frequency Tables and Graphs
   • Measures of Central Tendencies, Dispersion, Percentiles
   • Probability through Conditional Probability and the Use of Venn Diagrams and Tree Diagrams to Solve Problems
6. Calculus (20 hours)
   • Informal Idea of Limit and Convergence
   • Derivatives of Polynomials, Sine, Cosine, Tangent, Natural Logarithms and Exponentials base e through sums and chain rule
   • Application of First Derivative - Tangents, Minima and Maxima, Velocity an Acceleration
   • Indefinite Integration as Anti-differential then with Boundary Condition to Determine Constant
   • Definite Integration and Area under Curve

Part II: Options (35 hours)

Candidates are required to study all the sub-topics in one of the following options.

1. Statistical Methods
   • Normal Distribution
   • Random Samples, Standard Error, Confidence Intervals
   • Significance Testing
   • Contingency Tables, Chi Squared Test
   • Bivariate Data, Covariance, Correlation and Least Squares Regression Line
2. Further Calculus
   • Product and Quotient Rule for Differentiation, Differentiation of general Logarithmic and Exponential Functions
   • Graphing Functions including Use of Second Derivative and Behavior for large x to Find Asymptotes
   • Integration using u substitutions
   • Iterations through Newton-Raphson
   • Trapezium Rule for Estimation of Value of Definate Integral
3. Further Geometry
   • Transformations in the Plane through Composition, Inverse and Isometries
   • Vector and Matrix Representations of Transformations and Linear Combinations
   • Matrix Algebra through Inverse, Inverse of Compounds and Determinants
   • Origin Invariant and Non-origin Invariant Transformations

Portfolio (10 hours)

Five assignments, based on different areas of the syllabus, representing the following three activities:

• Mathematical Investigation
• Extended Closed-Problem Solving
• Mathematical Modelling